Historical research guide · 0819 · 2008
Observation of negative-frequency waves in a water tank: a classical analogue to the Hawking effect?
Germain Rousseaux · Christian Mathis · Philippe Maïssa · Thomas G Philbin · Ulf Leonhardt
In one minute
Hawking’s 1974 result says a black hole glows, and the classical engine underneath the glow is a mode conversion: a wave traced back to a horizon turns out to have come from two waves, one of positive and one of negative frequency, and mixing those two is what creates particles. Rousseaux, Mathis, Maïssa, Philbin and Leonhardt went looking for that conversion in the cheapest medium there is — water. In a 30-metre wave tank at the ACRI Génimar laboratory near Nice they drove a train of surface waves upstream against a counter-current running over a submerged ramp. Where the flow speed matches the speed at which the waves carry energy, waves can no longer swim upstream: that is a white-hole horizon, a black hole run backwards in time. Filming with three cameras, they recorded waves whose lines of equal phase lean the wrong way in a space-and-time plot, which is the signature of a negative-frequency wave. They report it as the first direct observation of the conversion — and note that it is much stronger than their model predicts.
Connection
Chapter 5 treats the vacuum as a fluid; this paper is the proof that the trade works in the other direction too, because a bucket of water reproduces the horizon physics that astrophysics can only infer. It puts a key ingredient of quantum particle creation on a bench you can walk around, film, and rebuild.
From the source
The classical root of Hawking radiation is a mode conversion: an escaping wave packet traced backwards in time originates from two distinct waves, one oscillating at positive and one at negative frequency, and because positive frequencies carry annihilation and negative frequencies creation, any process that mixes them creates particles in entangled pairs.Sect. 1, paragraphs 2–3; figures 1 and 3
In a moving medium a wave that can no longer travel upstream converts partly onto a branch with negative wavenumber, whose frequency measured in the frame drifting with the fluid is negative; such a wave cannot be launched directly, because its group velocity in the laboratory points back downstream, so seeing one is itself evidence that conversion occurred.Sect. 2, Doppler relation (2) and group velocity (3); figure 5
Water in a channel with an immersed ramp is an exact analogue of wave propagation in a curved space-time geometry as long as the wavelength stays well above the channel depth, so the depth of the water plays the role the Planck scale plays in astrophysics — a laboratory analogue where the short-wavelength physics is known rather than guessed.Sect. 3, dispersion relation (4), citing Schützhold and Unruh 2002
In the 30-metre ACRI wave tank, with a counter-current over a ramp, the team recorded waves carrying the negative phase slope that marks a negative-frequency wave, repeating at the period of the wave-maker — the first direct observation of positive-into-negative frequency conversion in a moving medium.Sect. 4; figure 8(b) and its time traces
Conversion into the negative-frequency branch does not require a horizon: numerical wave-packet simulations using Unruh’s method reproduce it for a flow that never blocks the packet, and the cleanest experimental data likewise came from flows just below the blocking condition, where breaking and turbulence are far weaker.Sect. 5, flow profile (5) and wave equation (6); figure 9
The measured conversion is significantly stronger than the simple one-dimensional model predicts, and the authors ask openly whether a nonlinear fluid-mechanics mechanism at the steepening wave crests enhances the analogue Hawking effect — the named follow-up is an experiment able to characterise the conversion process in detail.Sect. 6, Conclusions
The way in
https://doi.org/10.1088/1367-2630/10/5/053015How to cite it
Germain Rousseaux, Christian Mathis, Philippe Maïssa, Thomas G Philbin, Ulf Leonhardt (2008) Observation of negative-frequency waves in a water tank: a classical analogue to the Hawking effect? doi:10.1088/1367-2630/10/5/053015